logarithmic transformation from exponential to linear equation

Question

How to convert this exponential equation to linear equation.

$Y =\exp(17.9348)\cdot x^{-2.705}$

what I did is: $Y =\log(17.9348)-2.705\log(x).$

I am confused with this one: $Y=17.9348-2.705\log(x).$

Which one is correct transformation?

Thanks in advance!

Answer 1

The answer is neither! You need to take the logarithm of both sides: \begin{align*} y&=e^{17.9348}\,x^{-2.705} \\ \ln(y)&=\ln\left(e^{17.9348}\,x^{-2.705}\right) \\ \ln(y)&=\ln\left(e^{17.9348}\right)+\ln\left(x^{-2.705}\right) \\ \ln(y)&=17.9348-2.705\ln(x). \end{align*}